365 lines
11 KiB
C
365 lines
11 KiB
C
/* -- translated by f2c (version 19940927).
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You must link the resulting object file with the libraries:
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-lf2c -lm (in that order)
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*/
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#include "f2c.h"
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/* Table of constant values */
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static doublecomplex c_b1 = {0.,0.};
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static doublecomplex c_b2 = {1.,0.};
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static integer c__3 = 3;
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static integer c__1 = 1;
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/* Subroutine */ int zlagsy_(integer *n, integer *k, doublereal *d,
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doublecomplex *a, integer *lda, integer *iseed, doublecomplex *work,
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integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8,
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i__9;
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doublereal d__1;
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doublecomplex z__1, z__2, z__3, z__4;
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/* Builtin functions */
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double z_abs(doublecomplex *);
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void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
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/* Local variables */
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static integer i, j;
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static doublecomplex alpha;
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extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *,
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doublecomplex *, integer *, doublecomplex *, integer *,
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doublecomplex *, integer *), zscal_(integer *, doublecomplex *,
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doublecomplex *, integer *);
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extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
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doublecomplex *, integer *, doublecomplex *, integer *);
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extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
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doublecomplex *, doublecomplex *, integer *, doublecomplex *,
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integer *, doublecomplex *, doublecomplex *, integer *),
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zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *,
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doublecomplex *, integer *), zsymv_(char *, integer *,
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doublecomplex *, doublecomplex *, integer *, doublecomplex *,
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integer *, doublecomplex *, doublecomplex *, integer *);
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extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
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static integer ii, jj;
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static doublecomplex wa, wb;
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static doublereal wn;
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extern /* Subroutine */ int xerbla_(char *, integer *), zlacgv_(
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integer *, doublecomplex *, integer *), zlarnv_(integer *,
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integer *, integer *, doublecomplex *);
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static doublecomplex tau;
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/* -- LAPACK auxiliary test routine (version 2.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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September 30, 1994
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Purpose
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=======
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ZLAGSY generates a complex symmetric matrix A, by pre- and post-
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multiplying a real diagonal matrix D with a random unitary matrix:
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A = U*D*U**T. The semi-bandwidth may then be reduced to k by
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additional unitary transformations.
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Arguments
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=========
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N (input) INTEGER
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The order of the matrix A. N >= 0.
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K (input) INTEGER
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The number of nonzero subdiagonals within the band of A.
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0 <= K <= N-1.
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D (input) DOUBLE PRECISION array, dimension (N)
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The diagonal elements of the diagonal matrix D.
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A (output) COMPLEX*16 array, dimension (LDA,N)
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The generated n by n symmetric matrix A (the full matrix is
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stored).
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LDA (input) INTEGER
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The leading dimension of the array A. LDA >= N.
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ISEED (input/output) INTEGER array, dimension (4)
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On entry, the seed of the random number generator; the array
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elements must be between 0 and 4095, and ISEED(4) must be
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odd.
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On exit, the seed is updated.
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WORK (workspace) COMPLEX*16 array, dimension (2*N)
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INFO (output) INTEGER
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= 0: successful exit
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< 0: if INFO = -i, the i-th argument had an illegal value
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=====================================================================
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Test the input arguments
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Parameter adjustments */
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--d;
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a_dim1 = *lda;
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a_offset = a_dim1 + 1;
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a -= a_offset;
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--iseed;
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--work;
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/* Function Body */
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*info = 0;
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if (*n < 0) {
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*info = -1;
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} else if (*k < 0 || *k > *n - 1) {
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*info = -2;
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} else if (*lda < max(1,*n)) {
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*info = -5;
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}
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if (*info < 0) {
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i__1 = -(*info);
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xerbla_("ZLAGSY", &i__1);
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return 0;
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}
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/* initialize lower triangle of A to diagonal matrix */
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *n;
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for (i = j + 1; i <= i__2; ++i) {
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i__3 = i + j * a_dim1;
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a[i__3].r = 0., a[i__3].i = 0.;
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/* L10: */
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}
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/* L20: */
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}
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i__1 = *n;
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for (i = 1; i <= i__1; ++i) {
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i__2 = i + i * a_dim1;
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i__3 = i;
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a[i__2].r = d[i__3], a[i__2].i = 0.;
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/* L30: */
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}
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/* Generate lower triangle of symmetric matrix */
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for (i = *n - 1; i >= 1; --i) {
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/* generate random reflection */
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i__1 = *n - i + 1;
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zlarnv_(&c__3, &iseed[1], &i__1, &work[1]);
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i__1 = *n - i + 1;
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wn = dznrm2_(&i__1, &work[1], &c__1);
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d__1 = wn / z_abs(&work[1]);
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z__1.r = d__1 * work[1].r, z__1.i = d__1 * work[1].i;
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wa.r = z__1.r, wa.i = z__1.i;
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if (wn == 0.) {
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tau.r = 0., tau.i = 0.;
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} else {
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z__1.r = work[1].r + wa.r, z__1.i = work[1].i + wa.i;
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wb.r = z__1.r, wb.i = z__1.i;
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i__1 = *n - i;
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z_div(&z__1, &c_b2, &wb);
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zscal_(&i__1, &z__1, &work[2], &c__1);
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work[1].r = 1., work[1].i = 0.;
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z_div(&z__1, &wb, &wa);
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d__1 = z__1.r;
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tau.r = d__1, tau.i = 0.;
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}
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/* apply random reflection to A(i:n,i:n) from the left
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and the right
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compute y := tau * A * conjg(u) */
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i__1 = *n - i + 1;
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zlacgv_(&i__1, &work[1], &c__1);
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i__1 = *n - i + 1;
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zsymv_("Lower", &i__1, &tau, &a[i + i * a_dim1], lda, &work[1], &c__1,
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&c_b1, &work[*n + 1], &c__1);
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i__1 = *n - i + 1;
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zlacgv_(&i__1, &work[1], &c__1);
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/* compute v := y - 1/2 * tau * ( u, y ) * u */
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z__3.r = -.5, z__3.i = 0.;
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z__2.r = z__3.r * tau.r - z__3.i * tau.i, z__2.i = z__3.r * tau.i +
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z__3.i * tau.r;
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i__1 = *n - i + 1;
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zdotc_(&z__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1);
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z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * z__4.i
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+ z__2.i * z__4.r;
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alpha.r = z__1.r, alpha.i = z__1.i;
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i__1 = *n - i + 1;
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zaxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1);
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/* apply the transformation as a rank-2 update to A(i:n,i:n)
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CALL ZSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1,
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$ A( I, I ), LDA ) */
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i__1 = *n;
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for (jj = i; jj <= i__1; ++jj) {
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i__2 = *n;
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for (ii = jj; ii <= i__2; ++ii) {
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i__3 = ii + jj * a_dim1;
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i__4 = ii + jj * a_dim1;
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i__5 = ii - i + 1;
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i__6 = *n + jj - i + 1;
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z__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[
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i__6].i, z__3.i = work[i__5].r * work[i__6].i + work[
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i__5].i * work[i__6].r;
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z__2.r = a[i__4].r - z__3.r, z__2.i = a[i__4].i - z__3.i;
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i__7 = *n + ii - i + 1;
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i__8 = jj - i + 1;
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z__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[
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i__8].i, z__4.i = work[i__7].r * work[i__8].i + work[
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i__7].i * work[i__8].r;
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z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - z__4.i;
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a[i__3].r = z__1.r, a[i__3].i = z__1.i;
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/* L40: */
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}
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/* L50: */
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}
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/* L60: */
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}
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/* Reduce number of subdiagonals to K */
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i__1 = *n - 1 - *k;
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for (i = 1; i <= i__1; ++i) {
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/* generate reflection to annihilate A(k+i+1:n,i) */
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i__2 = *n - *k - i + 1;
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wn = dznrm2_(&i__2, &a[*k + i + i * a_dim1], &c__1);
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d__1 = wn / z_abs(&a[*k + i + i * a_dim1]);
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i__2 = *k + i + i * a_dim1;
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z__1.r = d__1 * a[i__2].r, z__1.i = d__1 * a[i__2].i;
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wa.r = z__1.r, wa.i = z__1.i;
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if (wn == 0.) {
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tau.r = 0., tau.i = 0.;
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} else {
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i__2 = *k + i + i * a_dim1;
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z__1.r = a[i__2].r + wa.r, z__1.i = a[i__2].i + wa.i;
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wb.r = z__1.r, wb.i = z__1.i;
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i__2 = *n - *k - i;
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z_div(&z__1, &c_b2, &wb);
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zscal_(&i__2, &z__1, &a[*k + i + 1 + i * a_dim1], &c__1);
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i__2 = *k + i + i * a_dim1;
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a[i__2].r = 1., a[i__2].i = 0.;
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z_div(&z__1, &wb, &wa);
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d__1 = z__1.r;
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tau.r = d__1, tau.i = 0.;
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}
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/* apply reflection to A(k+i:n,i+1:k+i-1) from the left */
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i__2 = *n - *k - i + 1;
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i__3 = *k - 1;
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zgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i + (i + 1)
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* a_dim1], lda, &a[*k + i + i * a_dim1], &c__1, &c_b1, &work[
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1], &c__1);
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i__2 = *n - *k - i + 1;
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i__3 = *k - 1;
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z__1.r = -tau.r, z__1.i = -tau.i;
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zgerc_(&i__2, &i__3, &z__1, &a[*k + i + i * a_dim1], &c__1, &work[1],
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&c__1, &a[*k + i + (i + 1) * a_dim1], lda);
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/* apply reflection to A(k+i:n,k+i:n) from the left and the rig
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ht
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compute y := tau * A * conjg(u) */
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i__2 = *n - *k - i + 1;
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zlacgv_(&i__2, &a[*k + i + i * a_dim1], &c__1);
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i__2 = *n - *k - i + 1;
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zsymv_("Lower", &i__2, &tau, &a[*k + i + (*k + i) * a_dim1], lda, &a[*
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k + i + i * a_dim1], &c__1, &c_b1, &work[1], &c__1);
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i__2 = *n - *k - i + 1;
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zlacgv_(&i__2, &a[*k + i + i * a_dim1], &c__1);
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/* compute v := y - 1/2 * tau * ( u, y ) * u */
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z__3.r = -.5, z__3.i = 0.;
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z__2.r = z__3.r * tau.r - z__3.i * tau.i, z__2.i = z__3.r * tau.i +
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z__3.i * tau.r;
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i__2 = *n - *k - i + 1;
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zdotc_(&z__4, &i__2, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1);
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z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * z__4.i
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+ z__2.i * z__4.r;
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alpha.r = z__1.r, alpha.i = z__1.i;
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i__2 = *n - *k - i + 1;
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zaxpy_(&i__2, &alpha, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1)
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;
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/* apply symmetric rank-2 update to A(k+i:n,k+i:n)
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CALL ZSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1,
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$ A( K+I, K+I ), LDA ) */
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i__2 = *n;
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for (jj = *k + i; jj <= i__2; ++jj) {
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i__3 = *n;
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for (ii = jj; ii <= i__3; ++ii) {
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i__4 = ii + jj * a_dim1;
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i__5 = ii + jj * a_dim1;
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i__6 = ii + i * a_dim1;
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i__7 = jj - *k - i + 1;
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z__3.r = a[i__6].r * work[i__7].r - a[i__6].i * work[i__7].i,
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z__3.i = a[i__6].r * work[i__7].i + a[i__6].i * work[
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i__7].r;
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z__2.r = a[i__5].r - z__3.r, z__2.i = a[i__5].i - z__3.i;
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i__8 = ii - *k - i + 1;
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i__9 = jj + i * a_dim1;
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z__4.r = work[i__8].r * a[i__9].r - work[i__8].i * a[i__9].i,
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z__4.i = work[i__8].r * a[i__9].i + work[i__8].i * a[
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i__9].r;
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z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - z__4.i;
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a[i__4].r = z__1.r, a[i__4].i = z__1.i;
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/* L70: */
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}
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/* L80: */
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}
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i__2 = *k + i + i * a_dim1;
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z__1.r = -wa.r, z__1.i = -wa.i;
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a[i__2].r = z__1.r, a[i__2].i = z__1.i;
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i__2 = *n;
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for (j = *k + i + 1; j <= i__2; ++j) {
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i__3 = j + i * a_dim1;
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a[i__3].r = 0., a[i__3].i = 0.;
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/* L90: */
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}
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/* L100: */
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}
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/* Store full symmetric matrix */
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *n;
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for (i = j + 1; i <= i__2; ++i) {
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i__3 = j + i * a_dim1;
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i__4 = i + j * a_dim1;
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a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
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/* L110: */
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}
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/* L120: */
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}
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return 0;
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/* End of ZLAGSY */
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} /* zlagsy_ */
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